Magnetic atoms primarily exhibit the properties of magnetic dipoles. In addition to magnetic dipoles general, solid-state spins have electric quadrupoles and magnetic octupoles known as typical multipole degrees of freedom. Magnetic dipoles can be coupled to a magnetic field and are easily detectable. However, directly observing the characteristics of multipoles is challenging because of the practical limitations of external fields coupled with multipoles. Because a quadrupole can be coupled to strain fields induced by lattice deformations, we present a new magnetoacoustic resonance method for analyzing the multipoles of solid-state spins using an ultrasonic wave propagating on the surface layer of the lattice. Recent developments in acoustic measurements have increased the importance of fundamental theory for the direct observation of quadrupole characteristics using magnetoacoustic resonance.

In this study, we focus on the rich multipole physics of CeB₆, which may have originated from a crystal-field quartet of the Ce atomic state. A method to directly analyze multipoles is desirable. Ce quadrupoles can be coupled to strain fields driven by ultrasonic waves, and CeB₆ is a favorable candidate for testing our method. Using solely ultrasonic waves renders it difficult to realize high-frequency measurements, which are necessary in the case of CeB₆, owing to technical limitations arising from the increase in frequency. This challenging problem can be solved by combining acoustic and optical measurements, i.e., using microwaves with ultrasonic waves simultaneously, because the microwave frequencies can be increased sufficiently for experiments under relatively high magnetic fields. This method is inspired by the analogy of two-photon absorption transition using electromagnetic waves with two different frequencies.

Our method of using quadrupoles coupled with ultrasonic waves may result in the use of acoustically operating solid-state spins as qubits for quantum computers and can be used in various applications of quantum information technology. Additionally, this innovation in acoustic control may complement conventional methods of optical control. Another important application is quantum sensing, such as biomagnetism microprobes with high resolution at the nanoscale.

(Written by Mikito Koga on behalf of all authors)

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